Mad Observations: In widely varying areas, animals follow leaders. This behavior ranges from ants seeking food, through birds and butterflies migrating long distances, to human politics. In all of these cases, the followers have a strong tendency (and motivation) to keep following the established leaders; if they didn't, particularly in the non-human examples, things would quickly be very bad for them.
Mad Reference: Note: This is a not-yet-published letter, not a peer-reviewed paper. It's basically raw presentation of research, which is what arxiv.org is for. "Effective leadership in competition." Hai-Tao Zhang, Ning Wang, Michael Z. Q. Chen, Tao Zhou, and Changsong Zhou. Full text available from arxiv.org.
Mad Hypothesis: As the authors state it, "is it possible for the minority later-coming leaders to defeat the dominating majority ones and how?" In other words, the hypothesis they're attempting to disprove is "It is impossible for minority later-coming leaders to defeat the majority leaders." If they manage to disprove that, they'll also have the how covered.
Mad Experiment: The researchers used a "generic model of collective behavior, the Vicsek model." As far as I can find, this is a widely used model for motion. Specifically, in this model individual motions are aligned to the average of their neighbors. In other words, if you want to think of this research in a more global context than just motion, you have to make the assumption that the individuals you're targeting will tend to follow along with whatever the people near them are doing. However, "near them" could mean "politically near them," for example, so it's not necessarily a bad assumption. Remember that translation of "near them" when pondering the rest of the findings, though.
In this model, the researchers introduced "leaders," which were simply individuals that did not simply align themselves to their neighbors. The followers obeyed the "follow your neighbor" rule, but the leaders were set to either move right (the established leaders) or left (the newcomer leaders).
After establishing the model with the right-leaders + followers, the researchers introduced late-coming left-leaders in various patterns and with various distributions. They measured how well these patterns of left-leaders were able to overcome the movement direction established by right-leaders.
They All Laughed, But: The researchers found that the late-comers were able to change the direction of the group, but that their ability to do so could be predicted based on two factors: the spatial distribution of the leaders (how far apart groups of leaders were) and the clumping of the leaders (how close together the members of a group of leaders were). Higher values for either of those factors increased the chance that the left-leaders could overtake control of the group. And, of course, it helped if the right-leaders had lower values for those factors.
Mad Engineering Applications: What these researchers found is that two factors help in taking over control of a group: wide distribution of the individuals working to change the group, but tight clumping of change-introducing individuals. In other words, it's good to spread out your leaders, but give them allies to work with locally.
It's easy to accidentally keep too much of the geographic part of this model, though. For example, if you translate the findings to politics, you should translate all of the model to politics. If you want to spread an idea throughout a group, you need people idealogically clumped to help each other influence others who are close to them idealogically, but it helps to also have such groups spread out to different places on the idealogical scale.
I'd be interesting to see other ways mad engineers could find to adapt this model to other scenarios. If you think of any, let me know in the comments.